Monday, January 30, 2012

On religion, I lean towards deism, but consider its proof largely a problem in astrophysics.

-- Edward O. Wilson, Consilience (1998).

Professor Wilson would probably feel mortified to behold this bone-headed bon mot displayed naked and defenseless on the printed page, without the protection of dust-jacket accolades from fellow professors. Not wishing to be in any way hurtful, we therefore provide it a camouflage or protective coloration of similar sallies.

On the existence of Beauty, I remain an Aesthetic Minimalist, but consider the resolution of this trifling problem to be a mere matter for Optics.

-- Casey Stengel

The postulated existence of the material world is a challenging problem for further research. We propose to settle the matter one way or the other, by scientifically examining a hypothetical chunk of the stuff (a Twinkie, as chance would have it) in our up-to-date laboratories. But for that we shall require a very large grant indeed.

-- Professor von Milchmoustache

Whether it be true that Truth itself exists, as such, can only be resolved by an expedition to the North Pole, to determine whether, in point of empirical fact, snow is white. Should it turn out to be the color of polar-bear pee, then Tarski’s entire enterprise falls to the ground.

There is a reason why our principle ontological essay is titled “On What There Is” rather than “What the meaning of “Is” is”.

The Platonist position is Realism for mathematical truths, or patterns if you prefer. It is not committed to Objects in any well-defined sense. We may, for convenience, speak of them casually, but if challenged, are happy to retreat.

The position known as Ontological Phenomenalism maintains that physical objects are nothing but bundles of sensations. This leaves undetermined, what they were, before Ontological Phenomenalists strolled into the café.

Perceivables existed prior to any preceivers, other than their Maker. Whatever they were, they are yet (though we ourselves bring further matter to the table). The nub of the problem (assuming that the Meaning of Being will remain forever impenetrable -- whether because of the nature of the case, or because the problem is ill-posed) lies rather in that “they” -- the Roster of Things -- thus, on what there is, the 'is' part being largely presupposed and left unexamined. For, what counts for us as a material object is not predetermined in the total quantum equation of the cosmos, and their delineation does not produce bright outlines. From the unquestionably existent, but in many respects unfathomable or indeterminate, physical totality (the ἀπείρων of Anaximander), we ourselves parcel out chunks for the convenience of our calculations and our everyday life. For stock-keeping purposes, this item is a coffee-cup; for the purposes of materials science, a mass of atoms. For the chemist, this atom stands on its own, and enters into contracts with other atoms; for the physicist, it is a complexus of nucleons and electrons. And that nucleon is either a proton, or another complexus, of quarks. Which in turn …

Raphael: Anaximander, striving to figure things out

Sed- sileo. I won’t be diving down that bottomless rabbit-hole. Yet rest content, to nurse this darkling java, its surface glinting with Cusp Catastrophes, steaming and swirling in this Ontological Coffee-Cup. And to praise Him who all this hath made.

A short but splendid article in this morning’s Washington Post, written by a genuine historian (Harold Holzer), rather than the Gingrich ersatz (he’s not a historian, but he plays one on TV) deserves your attention. It concerns the Lincoln-Douglas debates, which everyone cites as a pinnacle and paradigm, but which very few actually know the least thing about. The truth is very different from what is conventionally peddled. The stereotype of that debate, thus, functions as a meme or mythogen in our Société du Spectacle. Read the real dope here:

Meanwhile, in the increasingly mano-a-mano knifefight known as the Republican Presidential Primary, the Romney camp has put out an ad that some are depicting as an inadmissible escalation, but which, calmly considered, is more like a return to a bit of fact. Instead of hiring some announcer paid by themselves, to utter -- who knows -- half-truths or some more exiguous fraction of same, they simply reproduce a segment of an actual NBC broadcast from 1997, reporting on the Gingrich ethics scandal.

Predictably, the Gingroids call foul. Remarkably, NBC has demanded that the ad be pulled. Apparently Tom Brokaw, like the prophet Muhammad (upon whom be peace) is too sacred to admit of depiction. (Would the New York Times, or the 9/11 Commission Report, holler objections if they were ever quoted?)

The NBC position is craven and absurd, a brain-belch of their lawyers. For the rest of us: Isn’t it nice to have some pre-spin testimony? However adequate or inadequate NBC news may be or have been, they did not know in 1997 -- not in our more agonized nightmares did any of us then imagine -- that this creature would, years later, actually be front-running for the Presidency.

Putin, as everybody knows, is a Chuck-Norris-dangerous buffed hardbody man of parts. Not that easy to take the man on. But these guys seem up to the task.

~

For those who just can't get enough of the swaggering Slavic Man of Steel, click here for an adoring photo as he struts through white water wearing nothing above the waist; along with the Leader's directives for your winter reading:

Thursday, January 26, 2012

Much of the most important and vital
work done in the last half-centurydepends [not upon experiment or brute calculation, but] upon new
ideas;and new ideas are
notoriously exceedingly difficult to grasp.

-- Louis J. Mordell, Reflections
of a Mathematician (1959), p. 11

We previously stated that mathematics is best characterized as the science, not of number, but of structure (or of pattern -- at this level of generality, either term will do). As MacLane phrases it:

This chapter introduces the idea of the formal in terms of certain basic structures: Set, transformation, group, order, and topology. With Bourbaki, we hold that Mathematics deals with such “mother structures”. Against the historical order, we hold that they arise directly from the basic stuff of Mathematics.

-- Saunders MacLane, Mathematics: Form and Function (1986), p. 7

That last bit, you will note, is unabashedly Platonist, counterposing contingent human praxis to transcendent time-independent Truth. (We discuss this contraposition here.)

But beyond that, or rather as an animating force within it, and distinguishing mathematics from such structure- or pattern-centered enterprises as architecture or the plastic arts, is the central role of ideas.

MacLane puts the matter well. Re the derivation of Hamilton’s equations from Lagrange’s:

What appears as a trick is in fact an idea -- an idea which must have been clear to Hamilton when he did it. But we claim that in general most of the formal tricks appearing in Mathematics are really ideas in disguise -- ideas presented as manipulations because the manipulations can be made explicit, while the ideas are a bit nebulous.

-- Saunders MacLane, Mathematics: Form and Function (1986), p. 284

In a previous series of essays, we put forward certain particular “mother ideas”. Here we reserve a meditation-space for musing about “Ideas -- the very idea”.

~

Hadamard comments on Rodin’s testimony that, throughout the process of sculpting, he must keep the “global idea” in mind, even while working on the smallest details; and that “this cannot be done without a very severe strain of thought.”

I do not feel that I have understood [a mathematical argument] as long as I do not succeed in grasping it in one global idea; and, unhappily, as with Rodin, this often requires a more or less painful exertion of thought.

-- Jacques Hadamard, The Psychology of Invention in the Mathematical Field (1945), p. 65

Hadamard scoffs at the account given by Souriau in his Théorie de l’Invention: “Does the algebraist know what becomes of his ideas when he introduces them, in the form of signs, into his formulae? Undoubtedly not,” but just turns the crank of mechanical calculation. Apparently Souriau never consulted an actual mathematician, says Hadamard: The mathematician trusts his idea, his insight, his intuition, more than he does his calculations, which after all are not infrequently in error (Hadamard confesses that he, like Poincaré, was but an indifferent numerical calculator): If these clash, you first redo the calculations, before tossing overboard the Idea that motivated the whole thing.

~

Hadamard then makes an excursus rather off the path of our principal inquiry; yet we shall follow him a little ways. He confronts the question of whether language be the key to thought; and waxes indignant at those who, like Max Müller, dogmatically assert that, without language, thought itself must needs collapse:

I had a first hint of this when I read in Le Temps (1911): “The idea cannot be conceived otherwise than through the word, and only exists by the word.” My feeling was that the ideas of the man who wrote that were of a poor quality.

-- -- Jacques Hadamard, The Psychology of Invention in the Mathematical Field (1945), p. 66

The devotees of this position point to the dual meaning of the early Greek word logos -- ‘word, language’ and ‘reason, thought’; and would by implication deny that our diminutive and prickly friend, the humble hedgehog, could really know One Big Thing or even a little weentsy one.

Hadamard, by contrast, is virtually a militant in the opposite camp: “I fully agree with Schopenhauer when he writes, ‘Thoughts die the moment they are embodied in words.” This even applies to algebraic symbolism: too cumbersome to actually think with; you mostly only use it when checking your work.

The Neothomist philosopher Etienne Gilson seconds the opinion of his countryman:

A contemporary philosopher goes even further: some ideas may be not only pre-linguistic, but even pre-conscious:

We may not be aware of our ideas. An idea in this sense is a tendency to accept routes of thought ... that we may not recognize in ourselves, or even be able to articulate.

-- Simon Blackburn, Being Good (2001), p. 3.

The epigram "We may not be aware of our ideas" is deliberately paradoxical. Blackburn means "idea", not in the sense of the completely conscious "I have an idea, let's...", but of something like the often tacit metaphysical underpinnings of mentation and investigation, which we treated of earlier. -- Blackburn extends this notion (in a way reminiscent of, but antedating, Freud): "A permanent strand in Christian thought is that we have no insight, or even lie to ourselves, about our heart's desires." (id., p. 30)

We close this excursus with an epigram of William Hamilton which Hadamard quotes:

Speech is thus not the mother,

but the godmother of knowledge.

~

The reason such musings lie off our main track, is that we are largely uninterested in psychology, or thought-processes, or any of the hunches & hiccups that fallen Man is heir to as he struggles to comprehend all that His hand hath made. The philosophers among the penguins have different cognitive quirks from ourselves, as they too strive to unravel the tragic mystery of all that lies above and beneath: what matters is the Creation, and not the creatures, save as we matter to Him.
As for thought and language: with Hadamard, we conceive that there are cognitive activities for which vocalization is neither required nor especially helpful: say, playing Go, or basketball.

There is an epigram, variously ascribed, that has always fascinated me:

“How can I know what I think

until I see what I say ?”

On the face of it, this would appear to be anecdotal evidence for the thought-needs-language thesis. But upon nearer inspection, it might argue rather the opposite: That thought rose or arose from some wordless region of the self, and only became an object to critical consciousness after having been concretized (and perhaps partly simplified or falsified) by transformation into words.

For us, the key question is to what extent an Idea -- one worthy of the majuscule -- can even be adequately expressed in our language. Certainly the higher mathematics cannot be expressed in ordinary human language. It has invented for itself a more or less arcane system of signs, obeying no human syntax; you may, if you like, par abus de langage, call that too a “language”, but it is no natural human language, but rather an aide-mémoire cobbled together to express ideas that observe their own semantics, call that language or not. Hadamard himself attests that human language does not serve him especially well, when he must express mathematical ideas. Whenever he must hold forth on a mathematical topic, even one of his own devising and thus, to him, abstractly clear as a bell, he must write out the text of his lecture beforehand, lest he be left gasping and groping for words.

There is another old adage, current among linguistic philosophers:

“Whatever can be meant

can be expressed.”

At this point we hear the shade of that crusty critic of Le Temps, growling: All that you mean, maybe.

~

Let us put the point even more starkly. Ask Not (we channel Kennedy here) whether our (necessarily human versions of) ideas could be adequately communicated to some other rational species. Ask whether the Idea, as pre-existent in Platonic paradise, has been adequately incarnated in us.

(There now swims within my vision the image of a category-theoretic Universal Object, with arrows slanting downwards this way and that, as in Blake’s great painting.)

~

This is becoming interesting. Hoping that your appetite has been whetted as well, we link to a couple of math-related installments of the “Any Ideas?” series:

We have tried to outline a capitalized or pregnant sense of the everyday word idea, which in most contexts certainly does not bear such freight. (“I’ve got an idea, let’s go get pizza.”) There is, however, another sense, which is still scientific/intellectual, yet which bears no Platonic or foundational flavor: what is sometimes called a “bright idea”. A bright idea is what causes a light-bulb to appear over the cartoon character’s head. And it does represent some genuine cleverness, though its success is by no means guaranteed (and in the case of Donald Duck, will almost certainly come to grief.)

This more powerful form of inductive construction can be deduced rather simply from the older form. The trick is to construct, not the sequence of values, but the sequence of partial functions…

-- Andrew Gleason, Fundamentals of Abstract Analysis (1966), p. 145

A “trick” is to an idea as tactics is to strategy.

Similarly:

We could prove the inequality by a limit argument from the known inequality for finite sums, but the following reasoning involves a very interesting technical device.

-- Andrew Gleason, Fundamentals of Abstract Analysis (1966), p. 195

~

We have noted before that, once you set out to focus on Ideas per se, you keep winding up back in mathematics -- if only because there are so many of them there. Yet more: In our own lifetime, math itself has spawned a subfield whose task, it would seem, is precisely the study and development of Ideas -- for their own sake, almost, and beyond such practicalities as computing the area of the field of Farmer Brown (or rather, Farmer Enkidu, since this concern goes back to Babylonia and beyond) or even its offspring, geometry, or the handmaiden of that, the calculus, or … This field is called Category Theory, which (as faithful readers of this tragic blog will already know) I do not personally understand: but do note, that a recent introduction to same (subtitled “A first introduction to categories” -- the style of the title is that of children’s books; and God willing, someday toddlers will study this stuff), by Lawvere & Schanuel, is titled:

Conceptual Mathematics

C’est un titre astucieux. For again (this is a phenomenon which we have treated, in these essays, under the label “faux-naïf”), on the surface this might seem to be one of those liberal-feelgood substitutions for the actual hard work of thought, meant to bolster the self-esteem of slow-learners; whereas in actual fact, it points at concepts -- what underlies such relatively superficial activities as real analysis, point-set topology, algebraic geometry (you with me, kids?), and all the rest.

Now, this last is in line with our theme of Our Friends the Integers, so we nursed a fragile hope, despite the precedent of the flat and mindless use of supposedly numinous numbers on “Lost” (along with the downspiral of that initially eye-pleasing series into rank incoherence). And despite the disappointment of last year’s Rubicon, which shares some motifs, and showed a glimmer of promise; but all eyes were dry when the series was canceled.

So, “Touch”… How is it? (Or rather: Was it; for I shall not be watching again.)

First, I am pleased to report, the show once again exemplifies the sort of linguistic fidelity that would have been unimaginable on television during the years when I was growing up -- for them, no more than a fake/comedic ‘German’ accent, and an occasional ‘French’ ooh-la-la. The scenes set in Iraq (which were the best, or least-worst, to my taste) were staged, not merely in Arabic, but in authentic Iraqi dialect.

For the rest, you may sift the rubble without turning up any trinket of interest.

For one thing, there were incredibly many vastly annoying ads. Does not Fox know that, for the Season Premiere, you’re supposed to first sucker-in an audience, get them hooked, and only later melt their minds to the consistency of Twinkie-filling?

But the main thing: There’s just nothing there. Anyone can toss up a bunch of unlikely co-incidences and go Ooooooh. As a rule, implausible coincidences count as a weakness of a plot. To turn these into a strength requires a very skilled hand indeed. Thomas Pynchon did a decent job of it in The Crying of Lot 49 (though I enjoyed that book much more as an adolescent, than I did when I re-read it as an adult). The shallow minds that put this mess together show no such skill.

~

It is furthermore possible -- though I shall not be tracking this to see -- that the series may develop in the direction of Disability Porn. There is a lengthy tradition of exploitative uplift, giving false hope to the suffering (whose cognitive faculties, understandably, are trumped by their emotions), e.g. “Lorenzo’s Oil.” (I would link to Wikipedia, yet, remarkably, neither the English nor French nor German versions make any follow-up reference as to whether the stuff actually works. Judge for yourself:

The direction the series might take is actually even more catagogic, suggesting that your autistic child may actually have nothing wrong with him at all, he is just “differently abled”, in fact a geeenius, who can foil terrorist attacks halfway around the globe with a blink of his eyelids.

Tuesday, January 24, 2012

It may seem pointless at this point -- Overtaken By Events -- since the Phallus from Texas is now swirling turd-like down the Toilet-bowl of History (I take the phrase from the unpublished manuscripts of Karl Marx), but anyhow, this week’s New Yorkerdoes a number on what’s left of him -- desecrates his memory, and defecates on his corpse (an operation in which it is rather the excreta which are defiled). Which of course we deplore, while relishing.

And from the same issue of that splendid magazine, an outing of Mutt Rimney et gang; read about it here.

We have had frequent occasion, on this blog, to make use of a fine and seasoned adjective, to wit: Quinean; meaning, ‘of, like, relating to, scented with the essence of, or singing hymns of eulogy to, Quine'. Now: Quine rhymes with spline, or sine, or affine; but Quinean -- ahh, that is another case entirely. The vowel is, let us not be curt, and say “short”, but rather: trim, and crisp, with the stressed vowel of those splendid very syllables. To form the word, you pout the lips just slightly, as though sampling and evaluating a particularly fine dry sherry at a soirée of the Philosophy Department; you do not open your mouth wi-i-i-de the way they do over at Sociology or Athletic Medicine. It rhymes, thus, with Augustinian, and with very little else; it is itself, in fact, an eminently Augustinian vocable, and ill-inclined to participate in any vulgar limericks or advertising jingles.

(And as for Quine -- who knows how they pronounce it, over in -- horresco referens -- Applied Mathematics; probably rhymes with "groin".)

Whether -ean be numbered among these, I have not bothered to investigate; but simply decree, ex cathedra, en tant que Editor of Pronunciation emeritus (thus with awe-inspiring authority), that it Shall Be Thus: KWINN-ee-an.

A few of Dr J's many grandchildren, living in rags in a heartless world

Many of you kind hearts, taking pity, mailed in these little miniature ships-in-a-bottle, the bottles in question being unfortunately not one of those venerable green-glass housings for single malt, but those winky-twinky plastic shot-of-gin thingies you get on budget airlines, totally tacky, with this little like, quasi ship thingie inside, only it wasn’t like “O my goodness how did the craftsman manage to assemble such a treasure in so tiny a space?”, because the plastic bottles had been visibly sliced open and stuffed with these rinky-dinky crackly-plastic party-favors or Jack-in-the-Box prizes and then re-sealed, not very expertly, with Scotch tape, or in one case with masking tape, which really defeats the whole purpose.

We mentioned our strategy for acquiring said yaught -- I mean yocht -- I mean yacht (dang that’s a tough word to spell!), to wit: just sell tonsandtonsandtonsandtons of books. But so far, we have only managed to sell ounceandounce of books (to which the underpriced weightless Nook and Kindle thingies contribute nary a mite or a mote).

We earlier presented an alternative path to fame and fortune: auctioning off a brand-new, virgin (never used) word of our own devisement, (to wit:)

with bidding to begin at one million (euros or pounds sterling, to taste; no dollars or pesos please). So far the auction action has been, shall we say, disappointing.

So, think about it: All you have to do is get a second mortgage on your house, and maybe sell off a superfluous child or two (which is the Romney Road to Riches, documented here), and YOU could be the owner of your Very Own Word !!!

borne most prominently by Mr. Gingrich’s eighty-second paramour (and third wife). The word derives from Greek,

καλλίστη

(transcribed kalliste), a feminine adjective of the superlative degree, meaning ‘most beautiful’. Whether this epithet accurately describes the ex-mistress/spouse-of-the-month of Mr. Potato-Puff, depends on your taste in helmet-haired bottle-blonde Barbies with smiles like a constricted sphincter. Such matters form no part of our scholarly concern; our aims here are purely philological.

The -ist suffix is actually cognate with the English ending -est, used likewise to form adjectival superlatives. That is, it does not form part of the root, which is simply kalli- ‘beautiful’. This root has no English cognate, but it does show up in an English word borrowed from the ancient Greek; to wit

callipygian

For anyone who knows this word, it surely figures among the top ten favorites. And its meaning is, um, well… that is to say… Fact is, we here at the World of Doctor Justice run a pretty trim ship: family-friendly, and dedicated to Wholesome American Values. Not that being callipygian is necessarily out of line with Wh.A.V., not at all, it’s just … Unlike certain strutting public adulterers, who parade their paramours while posing as a paladin of the Moral Majority (and who previously, squatting in hiding, and still reeking from the bed of lust, hurled stones at President Clinton) -- unlike such gentlemen, I say, we are reluctant to utter here on this site the least syllable that might bring a blush to a maiden’s cheeks -- either set of cheeks. And so we urge you simply to consult (provided you are over eighteen, and for purely lexicographic purposes) this sober and decorous encyclopedia article concerning classical scupture of the Hellenic isles,

A venerable Latin tag, but I don’t really buy it. If you spread yourself too thin, you run aground in the shallows: there is no intellectual depth in maintaining a brain-deck of file-cards à la book = Buch = livre = libro = kitâb …; and the question, “How many languages do you speak?” always makes me grind my teeth. (“No more than one at a time,” I sometimes growl.) Pursuing multilingualism as a fetish smacks of calculating-savants, quiz-winners, and that ilk. Antiquity had its Mithridates of Pontus; the ottocento, its Cardinal Mezzofanti: but these polyglots were by no means philologists.

Nonetheless:

There is a quiditas, a je-ne-sais-quoi, a haeccéité or quintessence, in each linguistic culture, sui generis and untranslatable. To steep yourself deeply in these, particularly in a language with a long and intricate written history, like Latin or Arabic, or (at somewhat shallower time-depth, but overtaking those in later laps) English, German, or French. Both at work and in my free time, I use other languages (a different mix depending on the context) nearly as much as I use English, and am the better for it. But the point is to go deep, one culture at a time, and not to display some multilingual multitasking like simultaneous tournament chess. I know many people employed as linguists who have never read through an entire book in the language that they work with, beyond Harry Potter in translation. That seems sad.

Anyhow, here is a review, from this morning’s New York Times, of a book on multilingualism, Babel No More, which makes a useful distinction between multilinguals and hyperpolyglots.

(And for a beautiful and elaborate painted depiction of that ancient toppled tower, along with some entertaining philology, click here.)

Hugo Schuchardt, best known as a Romance philologist, but who
studied a remarkable range of languages, not excluding Basque and Berber,
and indeed Arabic (which he traveled to Egypt to master) nonetheless wrote:

Note that this assessment did not, however, prevent him from
pioneering the study of the neither-this-or-that Mischsprachen known as
creoles;he even put in a good
wrord for those culturally decidedly slack-stringed confections -- not
foam-born but test-tube-engendered -- the artificial entities Esperanto and Volapük.

On the mist-enshrouded plains of Southern Carolina, His Inevitability met Mister Potato-Puff on the field of battle. And lost his brand-new rattle. He got evited; or, as the saying goes downromneyed. Swelling even beyond his usual soufflé proportions, His Newtitude cavorted in celebration with Callista, his eighty-second mistress (and third wife).

~

“Victory has a hundred fathers; defeat is an orphan.” But defeat and victory both have a thousand kibitzers, from the commentariat, with instant analyses. One I heard on NPR this morning as I was making coffee: Exit polls reveal that Southerly Carolingians didn’t mind the Bain bit, they just don’t like Romney personally. And the next headline I click on after logging on says “Romney hurt by Bain”. (“Which newspaper d’ya read?”, as The New Yorker used to say.)

Others pointed to a venemous video attacking the downromney phenomenon. Ironically given that his own SuperPac made that video, Newton was righteously-wrathfully denouncing the casting of aspersions during a political primary (admonishing a reporter who had asked an uncomfortable question, he rather grandly christened the Seven Dwarves' televisual mud-wrestling as a "Presidential Debate"). In any case, we ourselves can rest content that our own sober, balanced testimony has in no way impaired the political process; proof may be found in our judicious and learnèd essay,

Many voters were put off, not so much at Romney’s wealth per se -- such ressentiment is really not characteristic of Americans, mythologues of Horatio Alger, though we do tend rather to look askance at perinatal silver-spoons -- as at the blithe (and lying) way he talks about it, and the careless way in which this vulture/venture capitalist can toss out a line like ‘I like being able to fire people who provide services to me’. Now, he cried foul on this one, saying he’d been quoted out of context. And indeed, in a narrow sense, that’s true, though his choice of metaphor is still psychologically revealing. But there is a larger context in which The Mitt’s choice of words was exactly on-target; in this deeper sense, he did not misspeak.

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About the Author

David Justice studied French at the Sorbonne, mathematics and physics at Harvard and MIT, and math and linguistics at Berkeley.He is the author of The Semantics of Form in Arabic, in the Mirror of European Languages; and of the fictional worksI Don’t Do Divorce Cases (which includes stories originally published in Ellery Queen and Alfred Hitchcock Mystery Magazine) and Murphy on the Mount. He taught French at Berkeley, and linguistics at the University of Alberta, then worked at Merriam-Webster as Editor of Etymology (where he edited Webster’s Book of Word Histories) and as Editor of Pronunciation.He subsequently was editor-in-chief at Franklin Electronic Publishers.He is currently employed as a language analyst, and consultant for the University of Maryland. He lives with his bride of forty years, overlooking a peaceful lake.